Maher Abd El-Rahman Ibrahim Adam_Adam-Estorff Train reduction CAS_3470_Offprint 2005

14 Pages·2004·0.61 MB·English

ComputersandStructures83(2005)11–24
www.elsevier.com/locate/compstruc
Reduction of train-induced building vibrations
by using open and filled trenches
M. Adam a, O. von Estorff b,*
aDepartmentofCivilEngineering,FacultyofEngineering(Shoubra),ZagazigUniversity,El-HomsySt.,Kaha,13743El-Kalubia,Egypt
bModellingandComputation,HamburgUniversityofTechnology,EissendorferStrasse42,D-21073Hamburg,Germany
Received8October2003;accepted9August2004
Availableonline2November2004
Abstract
Anumericalinvestigationontheeffectivenessofopenandin-filledtrenchesinreducingthebuildingvibrationsdue
to passing trains is presented. Particularly, a two-dimensional soil-structure system containing the cross-section of a
railwayembankment,theunderlyingsoil,atrenchbarrierandanearbysix-storeybuildingisconsidered.Fortheanal-
ysis,atimedomaincoupledboundaryelement-finiteelementalgorithmisemployed.Unlikemostofthepreviousfor-
mulations,thismodelcompletelyconsidersthesoil-structureinteractioneffectsanddirectlydeterminestheeffectofthe
wavebarrieronthestructuralresponse.Theeffectsofgeometricalandmaterialpropertiesofthetrenchanditsbackfill
materialonthestructuralresponseareinvestigated.Theresultspointoutthatusingatrenchbarrier,areductionlevel
upto80%ofthebuildingvibrationsandinternalforcescanbeachieved.Increasingthedepthorthewidthofatrench
mayimproveits reductioneffect anda softerbackfill materialresults in abetter isolation effect.
(cid:1)2004Elsevier Ltd. Allrights reserved.
Keywords:Vibrationreduction;Trenchbarrier;Wavepropagation;Buildingvibrations;FEM;BEM
1. Introduction mitthevibrationstothestructuresviatheirfoundations.
These vibrations lie in the frequency range of 4–50Hz
Duetotraintraffic,machineoperations,piledriving, and may bring some structures to resonance with their
or blasting, ground vibrations are generated that may vertical modes [1–3]. This type of vibrations can be a
cause distress to adjacent structures and annoyance to majorproblemindenselypopulatedareasandforstruc-
residents. For instance, most of the vibration energy tures,whicharehousingsensitivemachinery.Therefore,
generated due to a train passage is carried by Rayleigh in many countries new environmental regulations have
wavesthatpropagateclosetothesoilsurfaceandtrans- been introduced placing some constraints on railway
operations. Consequently, the isolation of the traffic-
induced vibrations has become an important issue in
* Corresponding author. Address: Modelling and Compu-
recentyears.
tation, Hamburg University of Technology, Eissendorfer Str-
Generally,itispossibletopreventtheadverseeffects
asse42,D-21073Hamburg,Germany.Tel.:[phone];
ofthesevibrationsbyprovidingasuitablewavebarrier
fax:[phone]/2028.
E-mail addresses: [email protected] (M. Adam), between the source and the structure to be protected.
estorff@tu-harburg.de(O.vonEstorff). This system of vibration isolation can be classified into
0045-7949/$-seefrontmatter (cid:1)2004ElsevierLtd.Allrightsreserved.
doi:10.1016/j.compstruc.2004.08.010
12 M.Adam,O.vonEstorff/ComputersandStructures83(2005)11–24
two categories, source isolation and receiver isolation. trenches of semi-circular and rectangular shape in a
With source isolation barrier it is tried to reduce the two-dimensional soil profile, while Beskos et al. [17]
vibrations at their source. It should be installed sur- and Leung et al. [18,19] investigated open and filled
roundingthe vibration source orat close distanceto it. trenches in homogeneous and non-homogeneous soil,
Thereceiverisolationbarrier,ontheotherhand,usually respectively. Ahmad and Al-Hussaini [20] and Al-Hus-
isbuiltawayfromthesource,surroundingthestructure sainiandAhmad[21]concentratedonsimplifieddesign
tobeprotected.Stationarysourcesofvibration,e.g.ma- methodologies for wave barriers and vibration screens,
chines working with a certain frequency, can be effec- also looking at an active isolation of machine founda-
tively isolated by a source isolation barrier, whereas a tionsbyopentrenches[22].Trenchesfilledwithdifferent
receiver isolation barrier is effective for a wide variety materials are discussedin [23].
ofwave generatingsources. In all cases, however, it can be observed that the
Different types of wave barriers, varying from very boundary element method is not well suited for the
stiffconcretewallsorpilestoveryflexiblegascushions, modelingofirregulargeometriesorapossiblenon-linear
arediscussedin[4–7].Amongthem,both,openandin- materialbehaviorofsoftsoilsand/orstructuralfounda-
filledtrenchesarethemostcommoninpracticalapplica- tions. To overcome this drawback, several procedures
tion since they present effective and low cost isolation forcouplingfinitewithboundaryelementsorfinitewith
measures. infiniteelementshavebeenproposed,followingthepio-
Thepublishedliteraturerevealsthatinearlystudies, neering work of Zienkiewicz and his co-workers, who
efforts have been directed mainly towards analytical developed a FEM/BEM coupling scheme [24] as well
studies and some experimental works to investigate the as a combination of the FEM with infinite elements
problem of isolation by means of trench barriers. Only [25]. Thus von Estorff and Prabucki [26], for instance,
a few experimental studies present some design guide- used a FEM/BEM scheme for dynamic soil-structure
lines for particular cases, but they are rather limited in interaction including trench problems, while Yang
their scope. Woods [8] and Haupt [9,10], for instance, et al. [27,28] concentrated on a coupling of finite and
conducted a series of field tests, analytical studies and infinite elements applied to studythe reduction of train
laboratory model experiments in order to study the inducedvibrationsusingdifferenttypesofwavebarriers.
screening performance of open trenches and concrete Withtheexceptionofafew,mostofthepreviousre-
walls. Moreover, the wave diffraction by spherical and searcheshavemainlydealtwiththedevelopmentofdif-
parabolic obstacles has been studied analytically by ferentnumericalmethodologiesasatoolfortheanalysis
someresearchers[11,12].However,theclosedformsolu- ofvibrationisolationproblems.Parametricstudieshave
tions were confined to simple geometries and idealized been rather limited and mostly performed in the fre-
conditions. quency domain. Moreover, the reduction of the nearby
For this reason, various numerical methods were ground surface vibration amplitude was the major
used by many authors for solving wave propagation concern.
andvibrationreductionproblems.Forexample,Lysmer In this paper, the investigation is focused on the ef-
andWaas[13]employedthelumpedmassmethod,while fectsofusingtrenchbarriersforthereductionofnearby
Segoletal.[14]appliedfiniteelementsalongwithspecial building responses through a parametric study directly
non-reflecting boundaries to investigate the isolation in the time domain. The building is directly considered
efficiency of open and bentonite-slurry-filled trenches inthemathematicalmodelingandanalysis.Thecoupled
in a layered soil. Frequently, also the finite difference boundary element–finite element (BE–FE) algorithm
techniquewasusedtostudythescatteringofaRayleigh developedearlierbyAdametal.[29]isextendedtohan-
waveletbyarectangularopentrench[15].Nevertheless, dlethebuildingstructureas frameelements[30,31]and
an underlying bedrock has to be inevitably included in employedforthenumericalanalysisofthecurrentprob-
the analysis models along with some sort of artificial lem, some details are given in Appendix A. Therefore,
transmitting boundaries due to the numerical con- differentfromothers,thesoil-structureinteractioneffect
straintsof theabove mentioned methods. isautomaticallytakenintoaccountandtheeffectofthe
In the last two decades, the boundary element barrier on the structural response is obtained directly.
method(BEM)hasbeenappliedforasignificantportion Theresponseofthebuildingisgivenintermsofacceler-
ofthestudiesonwavepropagationproblems.Inpartic- ations and internal forces, which represent the most
ular, this method is very well suited to investigate the important design parameters forstructural engineers.
wave propagation in soils, since the radiation into the
ground (e.g. into a halfspace) is directly included in
the formulation. Many authors adopted the BEM for 2. Numericalmodel andconsideredparameters
the analysis of isolation effects of open and in-filled
trenches, investigating different types of soils. Thus A reinforced concrete six-storey building frame, as
Emad and Manolis [16] considered shallow open shown in Fig. 1, shall be considered in detail. Its width
M.Adam,O.vonEstorff/ComputersandStructures83(2005)11–24 13
Fig.1. Numericalmodeloftheconsideredsoil-structuresystemandthetimehistoryoftheappliedload.
is12manditsheightis18m.Thebuildingislocatedto Table1
the right hand side of a railway embankment. In the Material properties of the embankment-soil-trench-building
direction perpendicular to the considered two-dimen- system
sional profile, the spacing between the frames is as- Material Massdensity Shearwave Poisson(cid:1)sratio
sumed to be 4m. The distance from the centerline of q(t/m3) speed m(–)
the track to the left hand side of the building is V(m/s)
20m. The building foundation level is located at a Halfspace 2.00 0150 0.33
depth of 1.5m below the soil surface. Two alternative Embankment 2.00 0250 0.33
types of foundations are assumed. The first type con- Concrete 2.50 2400 0.20
sists of strip footings of 0.8m thickness. The second foundation
type is a raft foundation of the same thickness. All ele- Columnsand 2.50 2400 0.20
mentsofthebuildingframeareassumedtohaveauni- Girders
Soil–bentonite Variable Variable Variable
form cross-section of 0.30m breadth and of 0.60m
mixture (1.2,1.6,2.0) (30,60,90) (0.25,0.33,0.45)
thickness.
Thetopsurfaceoftherailwayembankmentislocated
at 1.5m above the soil surface of a homogeneous half-
space. The material properties of the halfspace, the underlyingsoilcontainingthetrench,thebuildingfoun-
embankment layer, the foundation, and the frame ele- dation and any sort of soil irregularity. This region is
ments are given in Table 1. A trench barrier of width discretized by means of plane strain solid elements.
W and depth D is assumed to be located at a distance The finite element mesh is shown in Fig. 1. The second
Lmeasuredfromthecenterlineofthetrenchtotheleft part consists of the building frame modeled using
handsideofthebuilding.ThetrenchwidthW,thedepth planeframeelements[30].Sincethesehavethreedegrees
D and the distance L are assumed to be variable of freedom at each node, special care must be taken
parameters. when coupling them with the solid elements of the
The soil-structure system shown in Fig. 1 is divided foundation, which have only two translational degrees
into a BEM and a FEM subsystem. The BEM subsys- of freedom per node. Therefore, the previously devel-
tem,modeledbyboundaryelements,isadomainrepre- oped time domain BE–FE algorithm [29] needed to
senting the uniform part of the underlying soil be modified to deal with the current problem. Herein,
(halfspace). The FEM subsystem is divided into two the rotational degrees of freedom at the connect-
parts. The first part is a domain including the wave ing nodes are condensed out during the solution of
source, i.e., the train track, and a certain part of the the governing equation of motion of the coupled
14 M.Adam,O.vonEstorff/ComputersandStructures83(2005)11–24
Table2 are not considered in this analysis. Only the structural
Geometricparametersofthetrenchbarrier response due todynamic loadswill bedetermined.
Parameter Assumedvalues(m) Each floor mass is assumed to be attached to the
floor girder to account for their inertial effects during
Distancefrombuilding 2.0,3.0,5.0,8.0
the dynamic analysis. The case of a building resting on
leftside(L)
strip footings is considered to be the reference case.
Depthoftrenchbelow 3.0,4.50,6.0,8.0
groundsurface(D) The building response is obtained in terms of internal
Widthoftrench(W) 0.50,1.0,1.50,2.0 axial force, shear force and bending moments. The left
hand side column C1, the left intermediate column C2,
and the first floor girder G1 are selected for the discus-
sion.Inaddition,theaccelerationisdepictedonthese-
system. Later on, after the solution at each time step,
lectedpointsA,B,CandE.Alldetailsofthegeometry
theyarerecovered.Suchadynamiccondensationproce-
canbe foundin Fig. 1.
dure is straightforward and can be found in detail, for
The absolute maximum values of the building re-
instance, in [30].
sponse are summarized in Table 3. The overall maxi-
Twoconcentratedlineloadsinahorizontaldistance
mum axial force occurs in the left hand side column
of1.8mtoeachotherareappliedsimultaneouslytorep-
C1whilethemaximumshearingforceandthemaximum
resentthetrainload.Thetimehistoryofeachloadcon-
bending moments can be observed in the intermediate
sistsoffourconsecutiveimpulses;eachimpulsehavinga
columnC2.Itisinterestingtopointoutthattheresult-
time duration of 0.02s and 1000kN in amplitude. The
ingmaximumdynamicaxialforcesinthecolumnsrepre-
time between each two consecutive impulses is 0.02s as
sent about 30% of the expected static service load on
shown in Fig. 1. This load combination posses a wide
column C1 and about 10% of the static service load on
frequency contents with a predominate range from 20
columnC2.Moreover,theresultingmaximumdynamic
to 35Hz, and a central frequency of about 27Hz [31].
bending moment in the girder G1 is comparable to the
This covers the frequency range that is expected to be
expected maximum static service bending moments.
causedbyaheavyaxletrainpassage[1,2].Intheanaly-
Since this moment is reversible, the bending action on
sis,atotaltimeperiodof0.75sisconsideredwhichisdi-
critical sections of the girder could be doubled due to
vided into 600 time steps with a duration of 0.00125s
the train passage. Concerning the vibrations, the maxi-
each.
mum vertical acceleration occurs at the upper storey.
Since most of the previous investigations have dealt
As expected, the maximum values of the accelerations
withaharmonicloadofasinglefrequency,itwascom-
are gradually decreasing towards the lower levels of
montorelateeachoftheabovementionedparametersto
the building. The lowest value can be observed in the
the Rayleigh wavelength L which depends on the ap-
r
plied frequency and the soil properties. For example,
some researchers propose the trench depth to vary be-
tween0.6L and1.33L andthetrenchwidthtobebuilt Table3
r r
Dynamicstructuralresponsesincaseofusingstripfootingsor
between0.1L and0.5L [8–10,18–22].Thetrainloadap-
r r raftfoundations
pliedinthecurrentinvestigation,however,coversawide
frequency range. Therefore, the values of the studied Location Action Strip Raft %
parameters need to be considered in an average sense footings foundation Reduction
inordertocoverthepredominantfrequencyrangegiven ColumnC1 Na 202.24 187.54 7.26
in Table2. Qb 29.80 24.69 17.10
Inthecaseofthein-filledtrenches,thebackfillmate- Mc 66.09 54.78 17.11
rial is a soil–bentonite mixture which is assumed to be ColumnC2 Na 98.42 19.91 79.77
muchsofterthanthenaturalsoil.Themassdensityqof Qb 32.56 30.31 6.91
the backfill material, its Poisson(cid:1)s ratio m, and its shear Mc 72.22 67.23 6.90
wavespeedVarealsoconsideredtobevariableparame-
GirderG1 Na 27.73 19.00 31.48
ters.TheinvestigatedvaluesaresummarizedinTable1. Qb 32.48 27.29 15.98
Mc 69.19 58.12 15.99
PointA Maximum 12.39 9.56 22.81
3.Analysis of the structural response
PointB vertical 6.29 5.31 15.58
PointC acceleration 4.88 4.03 17.40
First, the analysis is performed to determine the PointE (m/s2) 4.83 3.63 24.80
buildingresponseduetotheappliedtrainloadswithout a N=Axialforce(kN).
any trench barriers. The building frame is supposed to b Q=Shearingforce(kN).
be subjected to the usual dwelling static loads, which c M=Bendingmoment(kNm).
M.Adam,O.vonEstorff/ComputersandStructures83(2005)11–24 15
first storey (see Table 3), which indicates that during a the reduction in the shearing forces, only the axial and
trainpassage,theresidentslivingontheupperfloorswill shearingforces will bediscussedin what follows.
suffertheverticalvibrationmorethanthoseonthelower
floors. To find out the effect of the foundation type on 4.1.Effect ofthe trench depth
the dynamic behavior of the structure, the analysis is
performed assuming that the building is constructed For the purpose of this investigation, it is assumed
on a raft foundation without any trench barrier. The that the depth of the open trench varies between 3m
resulting response and the achieved reduction as a per- and8m.Itshouldbementioned,however,thattheopen
centageofthecorrespondingvaluesincaseofusingstrip trench can be considered as a limit situation, since in
footings are also givenin Table3. reality––depending on the soil condition––its vertical
Itisveryinterestingtoobserve,thattheuseofaraft sideswillneedspecialsupportingmeasureswhenexceed-
foundationgreatlyreducestheaxialforceincolumnC2: inga certain depth.
A reduction of up to 80% with respect to the original In Fig. 2, the resulting reduction of the maximum
value is ascertainable. Only a slight reduction effect of internal forces for different values of the trench depth
about 7% occurs in the axial force in column C1 and is depicted. As expected, it can be observed that for all
in the bending moments in column C2. A reasonable internal forces the achieved reduction is getting larger
reduction effect of about 16–30% can be observed in with an increasing depth of the trench. Generally, the
the case of the internal forces in the girder G1, of the reduction in the column axial force, which is more re-
shearing force, and of the bending moments in column latedtotheverticalvibration,islargerthanintheshear-
C1. Concerning the vertical accelerations of the floors, ing forces and the bending moment. In addition, the
the use of a raft foundation has reduced the maximum reduction in the columns axial forces is larger than the
values by 15–25% as given in Table 3. Therefore, it reductioninthegirderaxialforce.Theaxialforceincol-
can be stated that for buildings close to railway tracks, umnC1achievesareductionof35%foratrenchdepth
araftfoundation ispreferableandbetter thanthe strip of3mand80%foradepthof8m.Theaxialforceincol-
footings. However, additional costs need to be taken umnC2showsareductionof50%and80%forthesame
intoaccountandcomparedwiththecostsofothertypes depths,respectively. Theotherforcesgetreduction val-
of reductionmeasures. ues in the range of 10–50%. When the trench depth is
doubledfrom3mto6m,thereductionvalueisapprox-
imatelydoubledfor allforces.
In Fig. 3, the resulting time history of the vertical
4. Parametric studyof theopentrench accelerations at point A is shown, assuming no trench
aswellasatrenchof3mand6mdepth.Thefigureindi-
Theanalysisisperformedforthestructurewithstrip catesaconsiderablereductionintheaccelerationampli-
footings considering the existence of an open trench as tudes that achieve about 50% reduction in the case of
shown in Fig. 1. The geometric variables are varied as 3m depth and about 75% reduction in the case of 6m
given in Table 2. Note that when a certain parameter depth.Moreover,itcanbeobservedthatthereisatime
is investigated, the other two parameters are kept con- delayinthewavearrivalatthestructure,andthevibra-
stant. Therefore, unless otherwise specified, the depth tion possesses a different waveform for each case. The
D of the trench and its width W are taken as 4.5m time delay means that in the presence of a trench the
and 0.5m, respectively. The distance L between the waves travel a longer distance surrounding the trench.
trench and the building is assumed to be 2.0m. Since The altered waveform indicates that some sort of wave
the reduction in the bending moment is identical with interference and transformations have occurred along
80 80
Column C1
Column C2
%)60 60 Girder G1
n ( Shearing Force
uctio40 Axial Force 40
d
e
R20 20
0 0
3 4 5 6 7 8 3 4 5 6 7 8
(a) Depth of trench (m) (b) Depth of trench (m)
Fig.2. Reductionoftheinternalforcesduetodifferentdepthsoftheopentrench.(a)Reductionoftheaxialforce,(b)reductionofthe
shearingforce.
16 M.Adam,O.vonEstorff/ComputersandStructures83(2005)11–24
15
2s ) No trench
m/ 10 D = 3.0 m
n ( D = 6.0 m
o 5
ati
er 0
el
c
c -5
a
al
c -10
Verti -15
0.00 0.10 0.20 0.30 0.40 0.50 0.60
Time (s)
Fig.3. ReductionoftheverticalaccelerationatpointAduetodifferentdepthsoftheopentrench.
the wave path [28]. The vibrations at the other selected of0.5m,andabout70%forawidthof2m.Thismeans
pointsshowedsimilartrends.Therefore,thedetailsshall when the excavated trench volume is four times larger,
beomittedhere.Also,itshouldbementionedthatusing theachievedreductionisincreasingbyabout25%only.
a raft foundation as discussed in the previous section, Besides,thereductionratiosintheaxialforceincolumn
thereductionlevelsinforcesandaccelerationsarelower C2 and girder G1 get slightly higher with an increasing
thanthe onesmentioned herefor the stripfootings. width. Thus, it can be stated that increasing the depth
Based on the above findings, one can state that the of a trenchis moreeffectivethanchanging itswidth.
open trench reflects a portion of the surface Rayleigh InFig.5thetimehistoriesoftheverticalacceleration
wavesandenforcetheotherbodywavestotravelverti- atpointAaredepicted.Thecasesofa0.5manda1.5m
callydownwardsinsidethesoilleadingtoalongerwave trench are compared with the acceleration without a
pathand more attenuationfor the waves before hitting trench. In fact, only little differences in the acceleration
the foundation ofthe structure. Thiscauses a consider- amplitudes can be noticed in the two cases of using a
able reduction in the wave amplitude and changes the trench.Almostsimilarwaveformswithnotimedelayoc-
waveform of the transmitted vibrations, especially in curwhichindicatesthatincreasingthetrenchwidthhas
theverticaldirection.Fordeepertrenches,thiseffectbe- only little effect on the vibration and its reduction.
comesmorepronouncedandthereductionintheinter- Therefore, it is advisable to perform a feasibility study
nal forces increases. for each particular case to achieve the optimum width
anddepthofatrenchresultinginamaximumreduction
4.2.Effect ofthe trench width of the response withthe lowestcost.
Fig. 4 shows the resulting reduction in the internal 4.3. Effect of the distance between the trench and the
forces for different values of the trench width. The in- building
crease of the trench width results in an increase of the
achieved reduction. Similar to the trench depth effect, The internal force reduction obtained by the open
thereductionintheaxialforceislargerthanthereduc- trenchlocatedatdifferentdistancesLfromthebuilding
tionintheshearingforceandbendingmoment.Theob- isdepictedinFig.6.Asageneraltrend,forallforcesthe
tainedreductionincolumnC1isabout55%forawidth reduction value decreases with an increasing distance,
80 80
Column C1
%)60 60 Column C2
on ( Shearing Force Girder G1
cti40 40
u Axial Force
d
e
R20 20
0 0
0.5 1.0 1.5 2.0 0.5 1.0 1.5 2.0
(a)Width of trench (m) (b)Width of trench (m)
Fig.4. Reductionoftheinternalforcesduetodifferentwidthsoftheopentrench.(a)Reductionoftheaxialforce,(b)reductionofthe
shearingforce.
M.Adam,O.vonEstorff/ComputersandStructures83(2005)11–24 17
s )2 15
m/
10
n (
o
ati 5
er
el 0
c
c
al a -5 No trench
ertic -10 WW == 01..55 mm
V -15
0.00 0.10 0.20 0.30 0.40 0.50 0.60
Time (s)
Fig.5. ReductionoftheverticalaccelerationatpointAduetodifferentwidthsoftheopentrench.
80 40
Column C1
Column C2
%) 60 Axial Force 20 Girder G1
n ( Shearing Force
ctio 40
u
d 0
e
R 20
0 -20
2 4 6 8 2 4 6 8
(a) Distance from building (m) (b) Distance from building (m)
Fig.6. Reductionoftheinternalforcesduetodifferentdistancesfromthebuildingtotheopentrench.(a)Reductionoftheaxialforce,
(b)reductionoftheshearingforce.
except for the normal force in column C2. Moreover, of 2m and 8m are shown in Fig. 7(a) and (b), respec-
whenthe distance becomes morethan 4m (columnC1) tively. Again, the result without a trench is included in
and5m(columnC2),theshearingforcesandthebend- the comparison. It can be noticed that the acceleration
ingmomentssufferanadverseeffectandtheirvaluesare amplitude in the case of 8m distance is larger than the
amplifiedasindicatedbythenegativesignofthereduc- amplitude in case of 2m distance with elongated or
tion in Fig. 6(b). These internal forces are morerelated stretched wave cycles. Although the maximum ampli-
to the horizontal motionwhich mainly results from the tude of the acceleration in the case of 8m distance is
scattered waves in such cases where vertical loads are smaller than the maximum amplitude in the case of no
applied. trench, it has a smaller number of cycles for the same
The horizontal acceleration time histories and their elapsed time. Moreover, Fig. 7(b) implies that the fre-
frequency contents resulting at point A for a distance quency content amplitudes of the horizontal vibration
3 30
2Horizontal acceleration (m/s ) ---321012 NLL o== t28re..00n cmmh Fourier amplitude (gal.s)12000
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0 10 20 30
(a) Time (s) (b) Frequency (Hz)
Fig.7. HorizontalaccelerationsatpointAduetotheopentrenchlocatedatdifferentdistancesfromthebuilding.(a)Timehistories,
(b)frequencycontents.
18 M.Adam,O.vonEstorff/ComputersandStructures83(2005)11–24
in the caseof 8m distanceis amplified in the lower fre- and softer. The advantage of an in-filled trench is that
quency range (2–10Hz) which might be closer to the one can achieve larger trench depths with no need for
eigenfrequencies of the structure leading to a higher permanent lateralsupports of thevertical sides.
structural response. This would explain the observed Throughout the following studies, the mass density,
amplificationintheshearingforceandbendingmoment. theshearwavespeedandthePoisson(cid:1)sratiooftheback-
Another possible reason is that the scattered waves fillmaterialareintroducedasnewvariableparametersin
causedmoredifferenthorizontalmotionsatthefounda- addition to the previously mentioned geometric para-
tion levelleadsto higherinternal forces. meters. In order to relate the shear wave speed ratio
Based on the above observations, one can state that between the backfill martial and the original soil to a
the relatively long distance between the trench and the morepracticalparameter,theimpedanceratio(IR)that
building give more chances to the occurrence of wave is frequently used in geotechnical engineering is
interferences between the body and the surface waves. introduced here as:
Thismayleadtoare-amplificationofthepreviouslyre- IR¼q V =qV ;
ducedwavesandtoagenerationofmorescatteredhor- b b s s
izontalwaves.Itshouldbementionedthatinthecaseof whereqbandqsdenotethemassdensitiesofthebackfill
sourceisolation,thedistancebetweenthetrenchandthe materialandthesoil,respectively,andVbandVsarethe
buildingmightbelongerthaninthepresentcase.Onthe shearwavespeedsofthetwomaterials.Simply, IRcan
other hand, the trench barrier gets closer to the wave beusedtodeterminewhetherthetrenchbarrierissoftor
source and therefore might be more effective than con- hard,i.e.,IR<1meansthatthetrenchbarrierissofter
cluded bymanyresearchers[22,23,28]. thanthe surroundingsoil andvisa versa.
Thus, one can roughly divide the distance between
the wave source and the building into three zones. The 5.1. Effectsof geometricalparameters
firstzoneisclosetothebuildingwherethereceiveriso-
lationusinganopentrenchcouldbemoreeffective.The In what follows, the mass density of the bentonite–
second zone is the one close to the source where the soil mixture is assumed to be 1.2t/m3, its shear wave
source isolation using an open trench could be more speed is 30m/s and its Poisson(cid:1)s ratio is set to be 0.45.
advantageous.Finally,thethirdzoneistheintermediate These values result in an impedance ratio of IR=0.12,
distancebetweenthefirstandsecondzone.Heretheiso- which indicatesaverysoftbackfillmaterial.The effects
lationusinganopentrenchisnotveryefficientandmay of the in-filled trench depth, width and distance on the
evenleadtoanadverseeffect,i.e.,toanamplificationof reduction of the internal forces are shown in Figs.
thestructuralresponse.Theextentofeachzonedepends 8–10, respectively. As expected, the trends already
onthesoilconditions,thetypeofthestructure,andthe observedinthecaseofanopentrenchalsocanbenoted
natureof the appliedload. herein. Only some tolerances in the achieved reduction
levels become obvious. Comparing the results shown
in Figs. 2 and 8, it can be observed that the reduction
5.Parametric study ofthe in-filledtrench values obtained using an in-filled trench is only about
70–80%ofthecorrespondingreductionvaluesobtained
In this section, the analysis is performed assuming usinganopentrench.Thedifferencebetweenthereduc-
thatthetrenchbarrierisfilledwithabentonite–soilmix- tion levels of the two types of trenchesis reducedto be
ture, which is softer than the natural soil. Logically, a about 5–10% in the case of changing the trench width
softer barrier is expected to approach the condition of as could beseenfrom the comparison of Figs. 4and 9.
an open trench as the backfill material is made softer The most important difference is that there is no
80 80
Axial Force Column C1
Column C2
60 60 Girder C1
%)
n ( Shearing Force
ctio 40 40
u
d
e
R 20 20
0 0
3 4 5 6 7 8 3 4 5 6 7 8
(a) Depth of trench (m) (b) Depth of trench (m)
Fig.8. Reductionoftheinternalforcesduetodifferentdepthsofthein-filledtrench.(a)Reductionoftheaxialforce,(b)reductionof
theshearingforce.
M.Adam,O.vonEstorff/ComputersandStructures83(2005)11–24 19
80 80
Column C1
Column C2
%)60 60 Girder G1
ction (40 40 Shearing Force
u
d
e
R20 Axial Force 20
0 0
0.5 1.0 1.5 2.0 0.5 1.0 1.5 2.0
(a) Width of trench (m) (b) Width of trench (m)
Fig.9. Reductionoftheinternalforcesduetodifferentwidthsofthein-filledtrench.(a)Reductionoftheaxialforce,(b)reductionof
theshearingforce.
80 40
Axial Force Column C1
Column C2
%) 60 30 Girder G1
n (
ctio 40 20
u
d
Re 20 10 Shearing Force
0 0
2 4 6 8 2 4 6 8
(a) Distance from building (m) (b) Distance from building (m)
Fig.10. Reductionoftheinternalforcesduetodifferentdistancesfromthebuildingtothein-filledtrench.(a)Reductionoftheaxial
force,(b)reductionoftheshearingforce.
amplification in the shearing force with the increase of the case of an in-filled trench is similar to the case of
thedistancebetweenthebuildingandthein-filledtrench no trench with a certain time delay and reduced ampli-
asshowninFig.10.Instead,thereductionvaluetendsto tudes. Thus, it may be stated here that the existence of
approach zero as the distance between the trench and the soft backfill material permits a considerable part of
the buildingincreases. the waves to pass through the trench directly, although
The time history of the horizontal acceleration at with reduced wave speed. The in-filled trench does not
pointA,assumingL=8m,isdepictedinFig.11.There- strongly enforce the body waves to travel vertically
sults obtained in the caseof no trench,anopen trench, downwards into the soil. This behavior seems to pro-
and an in-filled trench are compared. Different from duce a smaller amount of scattered waves than in the
the case of an open trench, the vibration waveform in case of an open trench. Consequently, the generation
2s ) 3
n (m/ 2 L = 8 m
o
ati 1
er
el 0
c
c
a
al -1 No trench
nt
o Open trench
z -2
ori In-filled trench
H
-3
0.00 0.10 0.20 0.30 0.40 0.50 0.60
Time (s)
Fig.11. ComparisonbetweenthehorizontalaccelerationsatpointAduetotheopenandthein-filledtrench.
20 M.Adam,O.vonEstorff/ComputersandStructures83(2005)11–24
60 40
Column C1
Axial Force
Column C2
%)40 30 Girder G1
n (
ctio 20 Shearing Force
u
d20
e
R 10
0 0
0.10 0.20 0.30 0.40 0.10 0.20 0.30 0.40
Softer Harder Softer Harder
(a) Impedance Ratio (IR) (b) Impedance Ratio (IR)
Fig.12. Effectoftheimpedanceratioontheeffectivenessofthein-filledtrench.(a)Reductionoftheaxialforce,(b)reductionofthe
shearingforce.
80 40
Column C1 Shearing Force
Column C2
%)60 Girder G1 30
n (
ctio40 20
u
d
e
R20 10
Axial Force
0 0
0.7 0.8 0.9 1.0 0.25 0.30 0.35 0.40 0.45 0.50
(a) Mass Density Ratio (ρb/ρs) (b) Poisson's ratio (υb)
Fig. 13. Effect of the properties of the backfill materials on the effectiveness of the in-filled trench. (a) Effect of the mass density,
(b)effectofthePoisson(cid:1)sratio.
ofnewhorizontalwavesandamodificationofitschar- ilyconceivedsincetheopentrenchisjustaspecialcase
acteristics are alsoreduced. Thiscould explainthe time of in-filled trenchwithIR=0.
delay, the non-changed wave form observed in Fig. 11, Theeffectsofchangingthemassdensityoftheback-
and also the non-amplified shearing forces observed in fill material q as a ratioof the soilmass density q are
b s
Fig. 10. Moreover, this finding confirms the previous shown in Fig. 13(a). In fact, the mass density of the
explanations of Figs. 6 and 7 in the case of an open backfill can be adjusted by controlling the consistency
trench. ofthebentonite-soilmixture,butthemarginforvarying
the massdensityisrather narrowinpractice, therefore,
5.2.Effects ofthe backfill material properties thevalueofq /q isallowedtorangefrom0.6to1.Fig.
b s
13(b)showstheeffectofchangingthePoisson(cid:1)sratioon
Inwhatfollows,theanalysisisperformedforthecase the force reduction level. From both figures, it can be
ofanin-filledtrenchwithadepthof4.5andawidthof concludedthatthemassdensityaswellasthePoisson(cid:1)s
0.5m, which is located at a distance of 2m from the ratio only have a very slight influence on the effective-
building.Themassdensityofthebackfillmaterialisas- nessof anin-filled trench.
sumedto be1.2t/m3, andits Poisson(cid:1)s ratio isset to be
0.45.The shearwave speed ofthe halfspace soilis kept
constant, while the corresponding wave speed of the 6. Conclusions
backfill material is considered to be variable, taking
thevaluesgiveninTable1.Consequently,theresulting Adetailedinvestigationonthereductionofbuilding
impedanceratioIRvariesbetween0.12and0.36.Fig.12 vibrations due to a train passage using a trench barrier
depicts the resulting reduction values versus the imped- has been presented. A previously developed coupled
ance ratio IR. With the increase of IR, the achieved BE–FE algorithm was applied for an analysis directly
reduction value decreases drastically, indicating that in the time domain. The effectiveness of using open or
the softer trench is the more effective one. Noteworthy in-filledtrenchasareductionmeasurehasbeendemon-
is the fact that as IR approaches zero, the achieved strated through a representative parametric study.
reduction values approach the values given in Fig. 2 Dependingontheobtainedresults,thefollowingconclu-
fortheopentrenchwithdepthof4.5m.Thiscanbeeas- sionsmaybedrawn: